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Some further thoughts about spectral kurtosis, spectral L2/L1 norm, spectral smoothness index and spectral Gini index for characterizing repetitive transients

Mechanical Systems and Signal Processing, 2018
Abstract Thanks to the great efforts made by Antoni (Mech. Syst. Signal Pr. 20 (2006) 282–307), spectral kurtosis has been recognized as a milestone to characterize repetitive transients, especially bearing fault signals caused by bearing defects.
Dong Wang
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SPECTRAL STUDY OF THE INVERSE INDEX

Advances and Applications in Discrete Mathematics, 2018
Summary: Let \(G=(V, E)\) be a simple graph of order \(n\) and size \(m\) with maximum degree \(\Delta\) and minimum degree \(\delta\) and with no isolated vertices. The inverse index of \(G\) is defined as \[\operatorname{ID}(G)=\sum_{uv\in E}\frac{d^{2}_{u}+d^{2}_{v}}{(d_{u}d_{v})^{2}}, \] where \(d_u\) is the degree of the vertex \(u\in V(G)\).
Ramírez, Angel   +2 more
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Singularity-corrected spectral index method

IEE Proceedings - Optoelectronics, 1998
The spectral index method (SIM) for analysis of the rib waveguide in air is improved by including the singular behaviour of the principal field component in the vicinity of the reentrant corners, thereby giving the singular SIM (SSIM). This generally improves the value of the modal propagation constant as compared with more exact solutions.
A. Vukovic   +4 more
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Bispectral Index and Spectral Entropy in Neuroanesthesia

Journal of Neurosurgical Anesthesiology, 2006
Spectral Entropy (SpEn) is an alternative tool to the bispectral index (BIS) for monitoring depth of hypnosis. SpEn measures response entropy (RE) and state entropy (SE). This open-label prospective study was designed to evaluate SpEn and BIS in 20 patients undergoing elective supratentorial neurosurgery with craniotomy and resection of brain tumors ...
Pietro, Paolo Martorano   +2 more
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Refractive index and spectral models for gradient-index materials

Applied Optics, 1983
Models are presented which describe the refractive index and spectral variation of gradient-index materials. Classes of gradient which exhibit little or no variation with wavelength are predicted. These are termed achromatic gradients. Experimental verification of the models is presented in a following paper.
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The Spectral Flow and the Maslov Index

Bulletin of the London Mathematical Society, 1995
In this article are studied operators of the form \[ D_A={d\over dt}- A(t), \] where for each \(t\), \(A(t)\) is an unbounded, selfadjoint operator on a Hilbert space. It is proved that the operator \(D_A\) is Fredholm and its index is given by the spectral flow of the operator family \(\{A(t)\}_{t\in\mathbb{R}}\).
Robbin, Joel, Salamon, Dietmar
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